Kinetic Theory of Instability of the Electron Beam-Plasma System Taking into Account the Elastic Electron-Atomic Collisions for an Arbitrary Scattering Indicatrix

A kinetic theory of stability of a fast electron beam-gas-discharge plasma system under conditions when the electron mean free path relative to elastic collisions with atoms is of the order of the plasma dimension along the direction of the beam propagation is developed. It is assumed that the cross section of elastic electron-atom collisions is considerably higher than the cross section of inelastic processes with electrons. The dispersion equations for an arbitrary indicatrix of elastic electron-atom scattering are obtained. Despite the smallness of the cross section for inelastic scattering in comparison with elastic one, it is also necessary to consider inelastic processes when the plasma Knudsen numbers are less than 0.3. As the Knudsen number decreases beneath 0.3 the growth rate considerably decreases in the range of instability, because the role of elastic scattering of electrons by atoms increases.